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Area between Two Curves

Find the volu...

Question

Find the volume of the parallelopiped whose coterminals edges are represented by the vectors
$\begin{matrix} \to a =^i - 2^j +^3 \to b = - 2^i + 3^j - 4^k \to c =^i - 3^j + 5^k \end{matrix}$

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Solution

Consider the problem
as we know that area of parallelopiped whose three sides are $\to a, \to b$ and $\to c$ equal to

$∣ ∣ [\to a \to b \to c] ∣ ∣$

And as we have

$\begin{matrix} \to a =^i - 2^j + 3^k \to b = - 2^i + 3^j - 4^k \to c =^i - 3^j + 5^k \end{matrix}$

Now,

$∣ ∣ [\to a \to b \to c] ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 2 & 3 - 2 & 3 & - 4 1 & - 3 & 5 \end{matrix} ∣ ∣ ∣ ∣$

$= 1 (15 - 12) + 2 (- 10 + 4) + 3 (6 - 3)$

$= 3 - 12 + 9 = 0$
Hence volume $= 0$ sq. units

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Q. Find the volume of a parallelopiped whose edges are represented by the vectors :

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Q. The volume of the parallellopiped whose coterminal edges are

2^i - 3^j + 4^k,^i + 2^j - 2^k, 3^i -^j +^k

Find the volume of the parallelepiped whose coterminous edges are represented by vectors

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